Reconstructing words using queries on subwords or factors

Gwenaël Richomme (1, 2) , Matthieu Rosenfeld (1)

1 LIRMM | ESCAPE - Systèmes complexes, automates et pavages
2 UPVM - Université Paul-Valéry - Montpellier 3

We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k 2 n log 2 (n)) words. Two previous upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.

Domaines: Combinatoire [math.CO]; Mathématique discrète [cs.DM]

Gwenaël Richomme, Matthieu Rosenfeld. Reconstructing words using queries on subwords or factors. 2023. ⟨hal-03922190v1⟩